Problem: Solve for $x$ and $y$ using substitution. ${-5x-3y = -1}$ ${y = -3x-5}$
Solution: Since $y$ has already been solved for, substitute $-3x-5$ for $y$ in the first equation. ${-5x - 3}{(-3x-5)}{= -1}$ Simplify and solve for $x$ $-5x+9x + 15 = -1$ $4x+15 = -1$ $4x+15{-15} = -1{-15}$ $4x = -16$ $\dfrac{4x}{{4}} = \dfrac{-16}{{4}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -3x-5}\thinspace$ to find $y$ ${y = -3}{(-4)}{ - 5}$ $y = 12 - 5$ $y = 7$ You can also plug ${x = -4}$ into $\thinspace {-5x-3y = -1}\thinspace$ and get the same answer for $y$ : ${-5}{(-4)}{ - 3y = -1}$ ${y = 7}$